MCQ
If $n$ is a positive integer, then ${\left( {\frac{{1 + i}}{{1 - i}}} \right)^{4n + 1}}$=
- A$1$
- B$-1$
- ✓$i$
- D$ - i$
✓
Answer
Correct option: C.
$i$
c
(c)Since $\frac{{1 + i}}{{1 - i}} = \frac{{(1 + i)(1 + i)}}{{(1 - i)(1 + i)}} = i$
Therefore ${\left( {\frac{{1 + i}}{{1 - i}}} \right)^{4n + 1}} = {i^{4n + 1}} = i{i^{4n}} = i\,\,\,\,\,({i^{4n}} = 1)$.
(c)Since $\frac{{1 + i}}{{1 - i}} = \frac{{(1 + i)(1 + i)}}{{(1 - i)(1 + i)}} = i$
Therefore ${\left( {\frac{{1 + i}}{{1 - i}}} \right)^{4n + 1}} = {i^{4n + 1}} = i{i^{4n}} = i\,\,\,\,\,({i^{4n}} = 1)$.
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